Preheat oven to 400 degrees. Heat 2 tablespoons olive oil in an ovenproof skillet over medium heat. Sprinkle salt and pepper on both sides of pork chops; add to skillet. Saute until golden brown, about 2 minutes; flip. Cook 2 minutes more; place pan in oven. Roast until meat is cooked through and registers 155 degrees on an instant-read thermometer, about 5 minutes. Transfer to a platter.

Meanwhile, in a large saucepan, heat remaining 2 tablespoons olive oil over medium heat; add onion. Saute over medium heat until translucent and beginning to brown, about 6 minutes. Add apples; saute 4 minutes more. Add vinegar, raisins, ginger, mustard, and cayenne. Stir well to combine; cover. Continue cooking, stirring occasionally, until apples are very tender but hold their shape, about 3 minutes. Season with salt and pepper, and serve over pork chops.